# Tuition Discounting

I mentioned last week that another book on the high cost of college, Robert B. Archibald and David H. Feldman's Why Does College Cost So Much, provides two explanations for the rising cost of post-secondary education that fly in the face of conventional wisdom.

The first explanation is counter-intuitive only because of the challenges we humans have with non-obvious mathematical arguments. But if you follow along, it provides a valid reason for why we should ignore top-line sticker prices when we debate educational inflation.

If you are one of the parents who have to pay the full \$60,000+ per-year price to send your kid to Yale, it's probably cold comfort that the average price to attend that school is less than two-thirds of that high number. But given the nature of averages, if some people are paying full retail then a lower average can only mean that others are paying much less. And the difference between sticker price and what people actually pay is referred to as "tuition discounting."

You may refer to it by some other name, such as financial aid or scholarships. And while aid is supposed to trigger gratitude from recipients and scholarships is meant to make the receiver proud of their accomplishments, for purposes of economics you should put such price breaks into the same category of ones an appliance salesman might give you if you "Buy Now!"

And according to Archibald and Feldman, such discounting is the reason why list prices for colleges are so high. To illustrate this point, I'll borrow an example they use throughout their book, one involving a college that costs \$2,000,000 a year to run which enrolls a total of 100 students.

If such a school has a \$1,000,000 subsidy (from an endowment or government grant, say), then it must earn the other million it needs to operate from tuition, which translates to asking each of their 100 students for \$10,000 per year.

But what if the school wants to give half the student body a discount, dropping their price to \$9,000 for needy kids, for example? In that case, they cannot simply charge half the student body \$9K and the other half \$10K, since that would leave them with a deficit. Which is why this simple financial-aid model requires them to raise tuition to \$11,000, which would allow them to charge half the students \$9,000, by giving them a \$2,000 "scholarship" from a new \$11,000 list price that the unsubsidized half of the student body now needs to pay.

In other words, the more generous a school is with aid (either based on need or merit), the more its sticker price has to go up. Which means we should only be arguing over average prices when we debate the cost of higher education (even if undiscounted prices gives us such delicious outrage).

But wait, there's more! For the authors also use this simple model to prove that raising subsidies available to a school cannot lead to a rise in tuition. Given that this flies in the face of the Bennett Hypothesis that says that rising educational prices are a direct result of increases in financial aid and loans, this second counter-intuitive claim is worth exploring further.

So getting back to our hypothetical school, what happens if that institution receives an additional \$100,000 in subsidy (let's say from an increases educational appropriation from state government)?

In this case, the school has a choice. It can give all 100 students a discount, charging those who once paid \$11,000 per year just \$10,000 and reducing the other half's cost from \$9,000 to \$8,000. Or it could be more generous with just needier students, giving all 50 of them an additional \$2,000 off, shrinking their annual tuition to \$7,000 while the unsubsidized half of the student body still pays list (which stays at \$11,000). Alternatively, they could spend this new money on new programming and leave tuition pricing untouched.

Notice that none of these available choices leads to tuition going up (only down or staying the same). Which means that the rising (average) price of tuition cannot be a result of easy availability of aid money (i.e., subsidies -- the driver of rising tuition for the Bennett Hypothesis) but must be coming from somewhere else.

And that somewhere else (for Archibald and Feldman, anyway) is a different economic force that binds together college professors, lawyers and dentists: cost disease, the subject for next week's exploration of why college costs so freaking much.